Two Minimum Conditions

★ 8/10functions Extrema calculus Monotonicity Logarithms

Problem

Let

f(x) = \ln(ax + 1) + \frac{1-x}{1+x} \qquad (x \geqslant 0).

1. If the minimum value of $f(x)$ is $1$ , find the range of possible values of $a$ . 2. If the minimum value of $f(x)$ is $\ln 2$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms

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